Answer Worked Out

Details:

1. The endpoints are:
   • (0, 3, 0) to (2, 0, 0)
   • (0, 3, 0) to (0, 0, 4)
2. The displacement vectors are:
   • a  =  (2, 0, 0) - (0, 3, 0)  =  (2, -3, 0)^T
   • b  =  (0, 0, 4) - (0, 3, 0)  =  (0, -3, 4)^T
3. The lengths are:
   • |a|²  =   (2, -3, 0)^T ·  (2, -3, 0)^T  =  13
   • |b|²  =   (0, -3, 4)^T ·  (0, -3, 4)^T  =  25
4. The normalized vectors are:
   • a_u  =  (2, -3, 0)^T / √13
   • b_u  =  (0, -3, 4)^T / 5
5. The dot product is:
   • a_u · b_u  =  (2, -3, 0)^T · (0, -3, 4)^T / (5 √13)
   • =  9 / (5 √13)  =   0.49923
6. The angle is:
   • cosθ   =  0.49923
   • θ  =  arc cos 0.49923  =  60.051°